mixtures of Gaussians

The deVaucouleurs profile is a horror! Anyone who has tried to accurately sample it on a grid knows this horror: It requires enormous numbers of samples at small radius and at the same time samples out to enormous radius if you want total flux to be right (which you don't, but that argument is too annoying to make here). These issues could be eased if we never had to sample the deV profile, but only the seeing-convolved deV profile, which is well-behaved on all interesting scales in well-sampled imaging (by assumption). I have a solution to these problems, which is to make a mixture-of-Gaussians approximation to the deV profile. If you also have a mixture-of-Gaussians approximation to the point-spread function then seeing-convolution is analytic and you never have to render the unconvolved nasty thing. Lang and I started implementation of this approach in the Tractor today, but we are far from done. I am so excited about this technical breakthrough I might have to write a (highly obscure) paper about it.


  1. Not completely sure from your description if this is prior art, but it seems relevant: http://adsabs.harvard.edu/abs/2002MNRAS.333..400C

  2. Anonymous: Highly relevant! They are interested in general (what you might call non-parametric) fitting of real galaxies, while I am interested in making exp and deV and Sersic fitting (what you might call parametric fitting) far faster and more accurate. But this is definitely relevant.

  3. I've been toying with writing a Gaussian fitter for real galaxies. The current crop of codes does not play nice with constraining isophotal twist and total flux (because Gausses are truncated compared to Sersics). Additionally the fit always has lots of local minimums and none of them compute errors. Boo. Perhaps we can have a chat next time your at MPIA?